Topology optimization has long been an active research area within the field of engineering optimization. For example, topology optimization is described in Topology Optimization—Theory, Methods and Applications, by Bendsøe and Sigmund, Springer, Berlin (2004).
In general, this disclosure relates to design involving uncertainties, known generally as reliability based design optimization (RBDO). Since mid-2000 there has been increasing research on reliability based topology optimization (RBTO) considering uncertainties in loads, material, boundary geometry or fabrication. However, failsafe design has not been directly addressed in relation to topology optimization. Failsafe refers to structures that demonstrate sustained structural integrity under the condition that an arbitrary structural element fails. Designing structures to be failsafe is important in applications where structural failure is catastrophic, such as in aircraft and nuclear power plants, for example. Failsafe design philosophy is an important reason why flying is considered so safe today. Indeed, relatively few catastrophic aircraft accidents are due to structural failures
Topology optimization has seen fast growing adoption throughout many major industries since the turn of the millennium. This includes successful aerospace applications during development of the new generation airliners such as A380, 350 and B787. However, the inability of taking failsafe requirement into consideration is a significant limitation. In fact, as optimization process pushes material utilization to maximum efficiency, design tends to be less redundant in general. For example, results of topology optimization are often benchmarked against Michell trusses which, while highly efficient, are statically determinate with zero structural redundancy.